A piston$-$cylinder system is filled with air. Initially, the air is at $489$ kPa and $26\backslash$deg C$.$ Then air is expanded to $1\mathrm{.}9$ times its original volume. Air is assumed to be an ideal gas. Assume the expansion process is polytropic with polytropic exponent n $=1\mathrm{.}2.$

a$.$ Find the change in entropy using constant specific heats at $300$ K$.$

b$.$ Find the change in internal energy using constant specific heats at $300$ K$.$

c$.$ Find the change in entropy considering specific heats are temperature$-$dependent.

d$.$ Find the change in internal energy considering specific heats are temperature$-$dependent.